Multi-messenger prospects for black hole – neutron star mergers in the O4 and O5 runs

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Volume 686 (June 2024)

A&A, 686 (2024) A265

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Table 1.

Detection limits and predicted detection rates for O4 and O5, assuming our fiducial population model (SFHo EoS and χ_BH = 0) and three variations.

	GW	KN + GW			GRB afterglow + GW			GRB prompt + GW

		J	z	g	Radio	Optical	X-rays	Swift/BAT	Fermi/GBM
LVK O4
Limit	12	21	22	22	0.1	22	10⁻¹³	3.5	4
Rate SFHo, χ_BH = 0	$15 . 0_{- 8.8}^{+ 15.4}$ $15.0^{+15.4}_{-8.8}$	$0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$	$0 . 16_{- 0.10}^{+ 0.17}$ $0.16^{+0.17}_{-0.10}$	$0 . 16_{- 0.10}^{+ 0.17}$ $0.16^{+0.17}_{-0.10}$	$0 . 015_{- 0.009}^{+ 0.015}$ $0.015^{+0.015}_{-0.009}$	$0 . 002_{- 0.001}^{+ 0.002}$ $0.002^{+0.002}_{-0.001}$	$0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$	$0 . 002_{- 0.001}^{+ 0.002}$ $0.002^{+0.002}_{-0.001}$	$0 . 012_{- 0.007}^{+ 0.013}$ $0.012^{+0.013}_{-0.007}$
(θ_j = 15°)					( $0 . 011_{- 0.006}^{+ 0.011}$ $0.011^{+0.011}_{-0.006}$ )	( $0 . 001_{- 0.001}^{+ 0.001}$ $0.001^{+0.001}_{-0.001}$ )	( $0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$ )	( $0 . 007_{- 0.004}^{+ 0.007}$ $0.007^{+0.007}_{-0.004}$ )	( $0 . 044_{- 0.026}^{+ 0.045}$ $0.044^{+0.045}_{-0.026}$ )
Rate SFHo, χ_BH = [0, 0.5]	$16 . 1_{- 9.4}^{+ 16.6}$ $16.1^{+16.6}_{-9.4}$	$0 . 29_{- 0.17}^{+ 0.30}$ $0.29^{+0.30}_{-0.17}$	$0 . 54_{- 0.31}^{+ 0.55}$ $0.54^{+0.55}_{-0.31}$	$0 . 53_{- 0.31}^{+ 0.55}$ $0.53^{+0.55}_{-0.31}$	$0 . 06_{- 0.03}^{+ 0.06}$ $0.06^{+0.06}_{-0.03}$	$0 . 014_{- 0.008}^{+ 0.015}$ $0.014^{+0.015}_{-0.008}$	$0 . 08_{- 0.04}^{+ 0.08}$ $0.08^{+0.08}_{-0.04}$	$0 . 006_{- 0.004}^{+ 0.006}$ $0.006^{+0.006}_{-0.004}$	$0 . 04_{- 0.02}^{+ 0.04}$ $0.04^{+0.04}_{-0.02}$
(θ_j = 15°)					( $0 . 10_{- 0.06}^{+ 0.11}$ $0.10^{+0.11}_{-0.06}$ )	( $0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$ )	( $0 . 22_{- 0.13}^{+ 0.23}$ $0.22^{+0.23}_{-0.13}$ )	( $0 . 04_{- 0.02}^{+ 0.04}$ $0.04^{+0.04}_{-0.02}$ )	( $0 . 20_{- 0.12}^{+ 0.21}$ $0.20^{+0.21}_{-0.12}$ )
Rate DD2, χ_BH = 0	$19 . 0_{- 11.1}^{+ 19.5}$ $19.0^{+19.5}_{-11.1}$	$0 . 30_{- 0.18}^{+ 0.31}$ $0.30^{+0.31}_{-0.18}$	$0 . 56_{- 0.33}^{+ 0.57}$ $0.56^{+0.57}_{-0.33}$	$0 . 54_{- 0.32}^{+ 0.56}$ $0.54^{+0.56}_{-0.32}$	$0 . 03_{- 0.02}^{+ 0.04}$ $0.03^{+0.04}_{-0.02}$	$0 . 007_{- 0.004}^{+ 0.007}$ $0.007^{+0.007}_{-0.004}$	$0 . 04_{- 0.02}^{+ 0.04}$ $0.04^{+0.04}_{-0.02}$	$0 . 003_{- 0.002}^{+ 0.003}$ $0.003^{+0.003}_{-0.002}$	$0 . 02_{- 0.01}^{+ 0.02}$ $0.02^{+0.02}_{-0.01}$
(θ_j = 15°)					( $0 . 04_{- 0.03}^{+ 0.05}$ $0.04^{+0.05}_{-0.03}$ )	( $0 . 004_{- 0.002}^{+ 0.004}$ $0.004^{+0.004}_{-0.002}$ )	( $0 . 11_{- 0.06}^{+ 0.11}$ $0.11^{+0.11}_{-0.06}$ )	( $0 . 2_{- 0.01}^{+ 0.02}$ $0.2^{+0.02}_{-0.01}$ )	( $0 . 12_{- 0.07}^{+ 0.12}$ $0.12^{+0.12}_{-0.07}$ )
Rate DD2, χ_BH = [0, 0.5]	$18 . 0_{- 10.5}^{+ 18.5}$ $18.0^{+18.5}_{-10.5}$	$0 . 97_{- 0.56}^{+ 0.99}$ $0.97^{+0.99}_{-0.56}$	$1 . 57_{- 0.92}^{+ 1.61}$ $1.57^{+1.61}_{-0.92}$	$1 . 55_{- 0.91}^{+ 1.60}$ $1.55^{+1.60}_{-0.91}$	$0 . 13_{- 0.07}^{+ 0.13}$ $0.13^{+0.13}_{-0.07}$	$0 . 03_{- 0.02}^{+ 0.03}$ $0.03^{+0.03}_{-0.02}$	$0 . 16_{- 0.09}^{+ 0.16}$ $0.16^{+0.16}_{-0.09}$	$0 . 012_{- 0.007}^{+ 0.012}$ $0.012^{+0.012}_{-0.007}$	$0 . 07_{- 0.04}^{+ 0.07}$ $0.07^{+0.07}_{-0.04}$
(θ_j = 15°)					( $0 . 21_{- 0.12}^{+ 0.21}$ $0.21^{+0.21}_{-0.12}$ )	( $0 . 03_{- 0.02}^{+ 0.03}$ $0.03^{+0.03}_{-0.02}$ )	( $0 . 55_{- 0.32}^{+ 0.57}$ $0.55^{+0.57}_{-0.32}$ )	( $0 . 09_{- 0.05}^{+ 0.09}$ $0.09^{+0.09}_{-0.05}$ )	( $0 . 5_{- 0.3}^{+ 0.5}$ $0.5^{+0.5}_{-0.3}$ )

LVKI O5
Limit	12	21	24.4	26	0.01	26	10⁻¹³	3.5	4
Rate SFHo, χ_BH = 0	$140_{- 81}^{+ 143}$ $140^{+143}_{-81}$	$0 . 08_{- 0.05}^{+ 0.08}$ $0.08^{+0.08}_{-0.05}$	$1 . 5_{- 0.9}^{+ 1.6}$ $1.5^{+1.6}_{-0.9}$	$2 . 1_{- 1.2}^{+ 2.1}$ $2.1^{+2.1}_{-1.2}$	$0 . 14_{- 0.08}^{+ 0.14}$ $0.14^{+0.14}_{-0.08}$	$0 . 05_{- 0.03}^{+ 0.05}$ $0.05^{+0.05}_{-0.03}$	$0 . 07_{- 0.04}^{+ 0.07}$ $0.07^{+0.07}_{-0.04}$	$0 . 008_{- 0.005}^{+ 0.008}$ $0.008^{+0.008}_{-0.005}$	$0 . 04_{- 0.02}^{+ 0.04}$ $0.04^{+0.04}_{-0.02}$
(θ_j = 15°)					( $0 . 23_{- 0.14}^{+ 0.24}$ $0.23^{+0.24}_{-0.14}$ )	( $0 . 07_{- 0.04}^{+ 0.08}$ $0.07^{+0.08}_{-0.04}$ )	( $0 . 18_{- 0.11}^{+ 0.19}$ $0.18^{+0.19}_{-0.11}$ )	( $0 . 03_{- 0.01}^{+ 0.03}$ $0.03^{+0.03}_{-0.01}$ )	( $0 . 15_{- 0.09}^{+ 0.15}$ $0.15^{+0.15}_{-0.09}$ )
Rate SFHo, χ_BH = [0, 0.5]	$136_{- 80}^{+ 140}$ $136^{+140}_{-80}$	$0 . 48_{- 0.28}^{+ 0.49}$ $0.48^{+0.49}_{-0.28}$	$5 . 6_{- 3.3}^{+ 5.8}$ $5.6^{+5.8}_{-3.3}$	$7 . 0_{- 4.1}^{+ 7.2}$ $7.0^{+7.2}_{-4.1}$	$0 . 81_{- 0.47}^{+ 0.83}$ $0.81^{+0.83}_{-0.47}$	$0 . 23_{- 0.14}^{+ 0.24}$ $0.23^{+0.24}_{-0.14}$	$0 . 33_{- 0.20}^{+ 0.34}$ $0.33^{+0.34}_{-0.20}$	$0 . 04_{- 0.02}^{+ 0.05}$ $0.04^{+0.05}_{-0.02}$	$0 . 20_{- 0.11}^{+ 0.20}$ $0.20^{+0.20}_{-0.11}$
(θ_j = 15°)					( $1 . 46_{- 0.85}^{+ 1.50}$ $1.46^{+1.50}_{-0.85}$ )	( $0 . 73_{- 0.43}^{+ 0.75}$ $0.73^{+0.75}_{-0.43}$ )	( $1 . 22_{- 0.71}^{+ 1.25}$ $1.22^{+1.25}_{-0.71}$ )	( $0 . 17_{- 0.09}^{+ 0.19}$ $0.17^{+0.19}_{-0.09}$ )	( $0 . 92_{- 0.54}^{+ 0.94}$ $0.92^{+0.94}_{-0.54}$ )
Rate DD2, χ_BH = 0	$144_{- 84}^{+ 148}$ $144^{+148}_{-84}$	$0 . 53_{- 0.31}^{+ 0.54}$ $0.53^{+0.54}_{-0.31}$	$6 . 8_{- 3.9}^{+ 6.9}$ $6.8^{+6.9}_{-3.9}$	$7 . 9_{- 4.6}^{+ 8.1}$ $7.9^{+8.1}_{-4.6}$	$0 . 55_{- 0.32}^{+ 0.56}$ $0.55^{+0.56}_{-0.32}$	$0 . 21_{- 0.12}^{+ 0.21}$ $0.21^{+0.21}_{-0.12}$	$0 . 27_{- 0.15}^{+ 0.27}$ $0.27^{+0.27}_{-0.15}$	$0 . 03_{- 0.02}^{+ 0.03}$ $0.03^{+0.03}_{-0.02}$	$0 . 17_{- 0.10}^{+ 0.17}$ $0.17^{+0.17}_{-0.10}$
(θ_j = 15°)					( $0 . 92_{- 0.54}^{+ 0.95}$ $0.92^{+0.95}_{-0.54}$ )	( $0 . 42_{- 0.25}^{+ 0.43}$ $0.42^{+0.43}_{-0.25}$ )	( $0 . 92_{- 0.53}^{+ 0.94}$ $0.92^{+0.94}_{-0.53}$ )	( $0 . 12_{- 0.06}^{+ 0.16}$ $0.12^{+0.16}_{-0.06}$ )	( $0 . 64_{- 0.37}^{+ 0.65}$ $0.64^{+0.65}_{-0.37}$ )
Rate DD2, χ_BH = [0, 0.5]	$144_{- 84}^{+ 147}$ $144^{+147}_{-84}$	$1 . 6_{- 0.9}^{+ 1.7}$ $1.6^{+1.7}_{-0.9}$	$13 . 4_{- 7.8}^{+ 13.8}$ $13.4^{+13.8}_{-7.8}$	$15 . 9_{- 9.3}^{+ 16.4}$ $15.9^{+16.4}_{-9.3}$	$1 . 9_{- 1.1}^{+ 2.0}$ $1.9^{+2.0}_{-1.1}$	$0 . 47_{- 0.28}^{+ 0.49}$ $0.47^{+0.49}_{-0.28}$	$0 . 71_{- 0.41}^{+ 0.73}$ $0.71^{+0.73}_{-0.41}$	$0 . 07_{- 0.04}^{+ 0.08}$ $0.07^{+0.08}_{-0.04}$	$0 . 4_{- 0.2}^{+ 0.4}$ $0.4^{+0.4}_{-0.2}$
(θ_j = 15°)					( $3 . 2_{- 1.9}^{+ 3.3}$ $3.2^{+3.3}_{-1.9}$ )	( $1 . 7_{- 1.0}^{+ 1.8}$ $1.7^{+1.8}_{-1.0}$ )	( $2 . 8_{- 1.6}^{+ 2.9}$ $2.8^{+2.9}_{-1.6}$ )	( $0 . 4_{- 0.2}^{+ 0.5}$ $0.4^{+0.5}_{-0.2}$ )	( $2 . 2_{- 1.3}^{+ 2.2}$ $2.2^{+2.2}_{-1.3}$ )

Notes. For the jet-related emissions, we assume a half-opening angle θ_j = 3.4°, while in parenthesis we report the rate assuming θ_j = 15°. The GW detection limits refer to the SNR_net threshold. Near infrared and optical limiting magnitudes are in the AB system; radio limiting flux densities are in mJy at 1.4 GHz; X-ray limiting flux densities are in erg cm⁻² s⁻¹ keV⁻¹ at 1 keV; gamma-ray limiting photon fluxes are in photons cm⁻² s⁻¹ in the 15−150 keV (Swift/BAT) or 10−1000 keV (Fermi/GBM) band. Detection rates are in yr⁻¹. The reported errors, given at the 90% credible level, stem from the uncertainty on the overall merger rate, while systematic errors are not included.

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